Problem: Simplify the following expression: $k = \dfrac{20xy - 10y^2}{10xy - 50zy} + \dfrac{20zy + 40y^2}{10xy - 50zy}$ You can assume $x,y,z \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20xy - 10y^2 + 20zy + 40y^2}{10xy - 50zy}$ $k = \dfrac{20xy + 30y^2 + 20zy}{10xy - 50zy}$ The numerator and denominator have a common factor of $10y$, so we can simplify $k = \dfrac{2x + 3y + 2z}{x - 5z}$